Timeline for Regarding the Thurston norm and the ways that a three-manifold can fiber over the circle
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2012 at 15:18 | vote | accept | Nick Salter | ||
| Aug 17, 2012 at 15:11 | comment | added | Lee Mosher | If a primitive class is represented by a disconnected fiber, say a 2-component fiber $F = F_1 \cup F_2$ then $F_1,F_2$ would be isotopic, because the monodromy map $F \mapsto F$ would have to transpose the two components (in general, with more components, the monodromy map would cyclically permute them). It would follow that $[F]=[F_1]+[F_2]=[F_1]+[F_1]=2[F_1]$. | |
| Aug 17, 2012 at 14:13 | comment | added | Nick Salter | Thank you for your answer. As I think about this more, I realize that the essential point that I'd like to understand better is why the fiber of a fibration associated to a primitive class is connected. I understand how the theorems in Thurston's paper establish the norm-minimality of fibers, but do they address connectedness? | |
| Aug 17, 2012 at 3:15 | history | answered | Lee Mosher | CC BY-SA 3.0 |